Igor A. Ushakov

Optimal Resource Allocation

With Practical Statistical Applications and Theory

• Gebundenes Buch

Produktbeschreibung

With an overview of different approaches to optimal resource allocation, from classical Lagrange methods to modern algorithms based on ideas of evolution in biology, this book details the applied methods of optimization, describes various methods of optimal redundancy problem solutions, and demonstrates how they can be solved with numerical examples and statistical methods. it is an ideal text for statistics and mathematics students as well as for students and practitioners in engineering and operations research.

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A UNIQUE ENGINEERING AND STATISTICAL APPROACH TO OPTIMAL RESOURCE ALLOCATION

Optimal Resource Allocation: With Practical Statistical Applications and Theory features the application of probabilistic and statistical methods used in reliability engineering during the different phases of life cycles of technical systems.

Bridging the gap between reliability engineering and applied mathematics, the book outlines different approaches to optimal resource allocation and various applications of models and algorithms for solving real-world problems. In addition, the fundamental background on optimization theory and various illustrative numerical examples are provided. The book also features:
An overview of various approaches to optimal resource allocation, from classical Lagrange methods to modern algorithms based on ideas of evolution in biology
Numerous exercises and case studies from a variety of areas, including communications, transportation, energy transmission, and counterterrorism protection
The applied methods of optimization with various methods of optimal redundancy problem solutions as well as the numerical examples and statistical methods needed to solve the problems
Practical thoughts, opinions, and judgments on real-world applications of reliability theory and solves practical problems using mathematical models and algorithms

Optimal Resource Allocation is a must-have guide for electrical, mechanical, and reliability engineers dealing with engineering design and optimal reliability problems. In addition, the book is excellent for graduate and PhD-level courses in reliability theory and optimization.

Produktdetails

• Verlag: Wiley & Sons
• 1. Auflage
• Seitenzahl: 256
• Erscheinungstermin: 8. April 2013
• Englisch
• Abmessung: 231mm x 155mm x 23mm
• Gewicht: 522g
• ISBN-13: 9781118389973
• ISBN-10: 1118389972
• Artikelnr.: 36729027

Autorenporträt

IGOR USHAKOV, DrSci, was previously a professor at both The George Washington University and the University of California, San Diego; chair of the Department of Large Scale Systems at the Moscow Institute of Physics and Technology; and a principal engineer at Qualcomm. In addition, he is founder of the International Group on Reliability's Gnedenko Forum and has authored or edited dozens of books and published more than 300 journal papers on reliability engineering, logistics, and quality assurance.

Inhaltsangabe

Preface xi 1 BASIC MATHEMATICAL REDUNDANCY MODELS 1 1.1 Types of Models 2
1.2 Non-repairable Redundant Group with Active Redundant Units 3 1.3
Non-repairable Redundant Group with Standby Redundant Units 7 1.4
Repairable Redundant Group with Active Redundant Units 10 1.5 Repairable
Redundant Group with Standby Redundant Units 13 1.6 Multi-level Systems and
System Performance Estimation 15 1.7 Brief Review of Other Types of
Redundancy 16 1.8 Time Redundancy 24 1.9 Some Additional Optimization
Problems 27 Chronological Bibliography of Main Monographs on Reliability
Theory (with topics on Optimization) 30 2 FORMULATION OF OPTIMAL REDUNDANCY
PROBLEMS 33 2.1 Problem Description 33 2.2 Formulation of the Optimal
Redundancy Problem with a Single Restriction 35 2.3 Formulation of Optimal
Redundancy Problems with Multiple Constraints 39 2.4 Formulation of
Multi-Criteria Optimal Redundancy Problems 43 Chronological Bibliography 45
3 METHOD OF LAGRANGE MULTIPLIERS 48 Chronological Bibliography 55 4
STEEPEST DESCENT METHOD 56 4.1 The Main Idea of SDM 56 4.2 Description of
the Algorithm 57 4.3 The Stopping Rule 60 4.5 Approximate Solution 66
Chronological Bibliography 68 5 DYNAMIC PROGRAMMING 69 5.1 Bellman's
Algorithm 69 5.2 Kettelle's Algorithm 73 Chronological Bibliography 84 6
UNIVERSAL GENERATING FUNCTIONS 85 6.1 Generating Function 85 6.2 Universal
GF (U-function) 87 Chronological Bibliography 94 7 GENETIC ALGORITHMS 96
7.1 Introduction 96 7.2 Structure of Steady-State Genetic Algorithms 100
7.3 Related Techniques 102 Chronological Bibliography 104 8 MONTE CARLO
SIMULATION 107 8.1 Introductory Remarks 107 8.2 Formulation of Optimal
Redundancy Problems in Statistical Terms 108 8.3 Algorithm for Trajectory
Generation 108 8.4 Description of the Idea of the Solution 111 8.5 Inverse
Optimization Problem 114 8.6 Direct Optimization Problem 124 Chronological
Bibliography 129 9 COMMENTS ON CALCULATION METHODS 130 9.1 Comparison of
Methods 130 9.2 Sensitivity Analysis of Optimal Redundancy Solutions 135 10
OPTIMAL REDUNDANCY WITH SEVERAL LIMITING FACTORS 142 10.1 Method of
"Weighing Costs" 142 10.2 Method of Generalized Generating Functions 146
Chronological Bibliography 149 11 OPTIMAL REDUNDANCY IN MULTISTATE SYSTEMS
150 Chronological Bibliography 170 12 CASE STUDIES 172 12.1 Spare Supply
System for Worldwide Telecommunication System Globalstar 172 12.2 Optimal
Capacity Distribution of Telecommunication Backbone Network Resources 179
12.3 Optimal Spare Allocation for Mobile Repair Station 183 Chronological
Bibliography 190 13 COUNTER-TERRORISM: PROTECTION RESOURCES ALLOCATION 191
13.1 Introduction 191 13.2 Written Description of the Problem 192 13.3
Evaluation of Expected Loss 195 13.4 Algorithm of Resource Allocation 197
13.5 Branching System Protection 201 13.6 Fictional Case Study 210 13.7
Measures of Defense, Their Effectiveness, and Related Expenses 217 13.8
Antiterrorism Resource Allocation under Fuzzy Subjective Estimates 223 13.9
Conclusion 232 Chronological Bibliography 232 About the author 235